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Chapter 5: Problem 140

If you are given a sequence that is arithmetic or geometric, how can you determine which type of sequence it is?

Short Answer

Expert verified
Determine the sequence type by examining the differences (for arithmetic) or ratios (for geometric) between consecutive terms in the sequence. If these are consistent, the sequence is arithmetic (for consistent differences) or geometric (for consistent ratios).

Step by step solution

01

Understand the Definitions

Define and comprehend the concepts of both sequences. An arithmetic sequence is a sequence of numbers where the difference between any two successive members is a constant. A geometric sequence in comparison, is a sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
02

Examine the Sequence

Inspect the provided sequence closely. Calculate the differences between each consecutive term if the sequence is suspected to be arithmetic. Likewise, calculate the ratios of consecutive terms if it is suspected to be geometric.
03

Rearrange and Compare

Collect all the differences or ratios calculated in the earlier step. For an arithmetic sequence, these differences should be the same (known as the common difference). For a geometric sequence, ratios between consecutive terms should be consistent (known as the common ratio).
04

Make a Conclusion

Based on Step 3, make a conclusion about the type of sequence. If the differences were equal, it's an arithmetic sequence. If the ratios were equal, it's a geometric sequence. If neither, it's neither arithmetic nor geometric sequence.

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Most popular questions from this chapter

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